Generalization of Zygmund type inequalities for the sth derivative of polynomials

Abstract

If p(z) is a polynomial of degree n and p(z) ≠ 0 in |z| < 1, it was proved by Hans and Lal [Anal. Math. 40, 105-115(2014)] that for any β ∈ C with |β| ≤ 1,1 ≤ s ≤ n, In this paper, we prove an inequality which gives an improved and generalized extension of the above inequality into Lγ norm.